This brings us to the physical: Power (force).

The father of the mathematics for mechanical forces is the Englishman Sir Isaac Newton(1643–1727). Some say he is a key figure in the Scientific Revolution of the 17th century.  

Thank you Wikipedia

It was he who finally captured nature in text and formula. His is a vast field so we will only venture as far as necessary for our purposes here.

His work:

If an exertion causes a response (change) then it is said a force is applied.

Only four main interactions are known: in order of decreasing strength, they are: strong (keeping nucleus together in an atom), electromagnetic (that's us!), weak (atomic radio-active decay), and gravitational.

FORCE: In the mechanical world:

F = m * dv/dt  = mass(kg) * acceleration (mtr/s²) N [Newton's second law of motion] remember this with the formula for weight:   F = mass * gravitational force N (g = 9.81mtr/s²)

What is a Newton? One Newton is the force needed to accelerate one kilogram of mass at the rate of one metre per second squared in the direction of the applied force.

Personal note: What is math visualisation?

When we use leverage of a pole to our advantage in real life we can except it as that's the way it is...or we can visualise it by saying:

If a stronger force is applied the resultant is bigger.

The longer the pole the resultant is also bigger.

To make it complete the visualisation we can also say: for the same amount of resultant if the pole is longer the applied force can be smaller (less work for me). 

Therefore there must be a resultant to the two "actions" that makes my work easier...lets call it - Torque (simply because those before us has called it by this name). 

T = Force * distance N.mtr.

Suddenly I don't have to remember what torque is...I just know it.

Same with just about any mathematical problem I am sure.

To complete the topic and honour the great and gifted Sir Isaac Newton.

I have since read - at least the introduction  -  Sir Isaac Newton's paper and with great emotion I reflect to the state of our world and how it could have been...not to mention what the future might hold.

Through all of this had the funniest job as mint master in England, Really? (Thank you Wikipedia and it was confirmed by the Royal Mint website.)?

Quoted from the book: Principia Mathematica - DEFINITION II.
 

This results in the formula F = mass (kg) * acceleration (m/s²)

Can you visualise this formula?

If you did then you have shared the same light as it has gone on for Newton in the sixteen hundreds.

How great is that!

Units of Energy

The unit of energy is named after James Prescott Joule.

Joule is a derived unit and it is equal to the energy expended in applying a force of one newton through a distance of one metre.

It is also the energy dissipated as heat when an electric current of one ampere passes through a resistance of one ohm for one second. It is named after the English physicist James Prescott Joule (1818–1889).

Energy is also measured in kilowatt-hours

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What is the difference between speed and velocity.

Velocity is the adhoc speed meaning for an increment of time (anytime in space) what distance was travelled ie v = distance / time.

Speed on the other hand is the calculation of the total distance travelled over time in a specified time i.e: S =the distance / time

Explain: Travel Town A to town B = 100km.

 After having arrived at town B we now have a time (say 1hr) then the speed travelled is S = 100/1 = 100km/hr, it does not consider the stops and start acceleration and deceleration.

On the other hand velocity goes deeper - one could say it is the sum of all the "DIFFERENT VELOCITIES" travelled. 

Speed = v1 + v2 + v3

The confusing thing is: - At the end of travelling the velocity works out exactly the same as speed.

I say, they are technically the same but mathematically not.

PS: Now that I think about it - speed should always be indicated in caps (S) but velocity as an instantaneous value should be always small caps(v).

In working with circles three (3) different methods apply -

Many text books confuse the hell out of me as to why they use what method when...I think they did not know themselves and simply lists both ways as if its one and the same.

Mathematically 2π (Pi) is definitely not equal to 360Degrees.

Graphically they are the same.

But 2 * Pi radians = 360 degrees...which implies 2*Pi*57.3 = 360 which is mathematically also true.

The radians has to be there to complete the equality so be careful. (At least for me it tells one in what format we are working)

1. The Pi method:- The relationship by natural law is that circumference of a circle/diameter = 3.142 and it is called Pi.
2. Degrees method - this is simply having the circle sliced in 360 degree segments in order to get an idea of how big a segment might be.
3. The radians method:- Section the circumference in radius sections and the slices we get are radians.  the purpose of this method is for calculations of angular velocity, e.g. how fast a rotating machine are spinning or instantaneous values at specific times.     

How do we tie them all together:

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A brilliant example of where the different methods are used is in the electrical waveform.

When we only care about the relations of spacing between units - we use angles.

When we want to know how fast a rotating unit is travelling (distance over time) (velocity) we use radians...that is angular velocity (rads/sec).